States and state functions

Certain of the macroscopic properties have fixed values for a particular state of the system, others do not. For example, suppose that we maintain 1 gram of water in a vessel at and 1 atmosphere pressure it will have a volume of 1 cm. These quantities specify the state of the system. Any time we satisfy these conditions we have the water in the same state and as long as it is in that state it will have these particular specifications. The macroscopic properties which we have mentioned—mass, pressure, temperature, and volume—are known as state functions or state variables. 

One important characteristic of a state function is that once we have specified the state of a system by giving the values of some of the state functions, the values of all other state functions are fixed. Thus, in the example just given, once we have specified the mass, temperature, and pressure of the water, the volume is fixed. So, too, is the total energy of the system, and energy is therefore another state function. When the concept of entropy is discussed in the next chapter we shall see that entropy is also a state function. 

Another important characteristic of a state function is that when the state of a system is altered, the change in any state function depends, only on the initial andjSn.aI states of the system, and not on the pathToilo.w.e.d m.making.tlie change- For example, if we heat our sample of water from 0° C to 25 C, the change in temperature is equal to the difference between the initial and final temperatures  

The wav in whic.h the..tem.perature.change is brought.about.has,riQ effect on this, result. 

This example may seem trivial, but it should be emphasized that not all functions have this characteristic. For example, the amount of heat supplied to a system in order to change it from one state to another varies with the way in which the change is brought about. Similarly, the work done by a system v/hen it passes from one state to another is not a fixed quantity, but depends upon the path. This will be discussed in greater detail later. 

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A uniform thermodynamic system—(uniform) body—may be visualized as a block of single (i.e., pure or one-constituent) material, the mass of which is fixed (closed system) with properties depending only on time (and not on space). Therefore, the state and state functions change only in time. Results (1.5) and (1.42) (where it is possible to use time integration) may be expressed in the rate form as it was explained at the end of Sect. 1.4. Consequently, such forms of energy balance and entropy inequality in uniform systems are [1, 3, 4]... 

This chapter begins by explaining some basic terminology of thermodynamics. It discusses macroscopic properties of matter in general and properties distinguishing different physical states of matter in particular. Virial equations of state of a pure gas are introduced. The chapter goes on to discuss some basic macroscopic properties and their measurement. Finally, several important concepts needed in later chapters are described thermodynamic states and state functions, independent and dependent variables, processes, and internal energy. 

Introduction to Thermodynamics States and State Functions The First Law of Thermodynamics Work and Heat... 

Calculation of thermophysical properties of gases relies on the principle of corresponding states. Viscosity and conductivity are expressed as the sum of the ideal gas property and a function of the reduced density ... 

The relationship between this M avefunction (sometimes called state function) and the location of particles in the system fonus the basis for a second postulate ... 

As one raises the temperature of the system along a particular path, one may define a heat capacity C = D p th/dT. (The tenn heat capacity is almost as unfortunate a name as the obsolescent heat content for// alas, no alternative exists.) However several such paths define state functions, e.g. equation (A2.1.28) and equation (A2.1.29). Thus we can define the heat capacity at constant volume Cy and the heat capacity at constant pressure as... 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

The are many ways to define the rate of a chemical reaction. The most general definition uses the rate of change of a themiodynamic state function. Following the second law of themiodynamics, for example, the change of entropy S with time t would be an appropriate definition under reaction conditions at constant energy U and volume V ... 

A partial acknowledgment of the influence of higher discrete and continuum states, not included within the wavefunction expansion, is to add, to the tmncated set of basis states, functions of the fomi T p(r)<6p(r) where dip is not an eigenfiinction of the internal Flamiltonian but is chosen so as to represent some appropriate average of bound and continuum states. These pseudostates can provide fiill polarization distortion to die target by incident electrons and allows flux to be transferred from the the open channels included in the tmncated set. 

B3.4.7.2 NUMERICALLY EXTRACTING BOUND STATES AND RESONANCE FUNCTIONS... 

This section attempts a brief review of several areas of research on the significance of phases, mainly for quantum phenomena in molecular systems. Evidently, due to limitation of space, one cannot do justice to the breadth of the subject and numerous important works will go unmentioned. It is hoped that the several cited papers (some of which have been chosen from quite recent publications) will lead the reader to other, related and earlier, publications. It is essential to state at the outset that the overall phase of the wave function is arbitrary and only the relative phases of its components are observable in any meaningful sense. Throughout, we concentrate on the relative phases of the components. (In a coordinate representation of the state function, the phases of the components are none other than the coordinate-dependent parts of the phase, so it is also true that this part is susceptible to measurement. Similar statements can be made in momentum, energy, etc., representations.)... 

Acetyl-i-carnitine (4) is marketed in Italy for dementia as of this writing it is also in Phase III clinical trials in the United States and Europe. In a double-blind, placebo-controUed clinical trial over a one-year period involving 130 patients with clinically diagnosed AD, a slower rate of deterioration in 13 of the 14 outcome measures was observed in the dmg-treated group (28). Earfler smaller scale pilot studies in demented patients had also shown some improvement of various behavioral and cognitive functions (29). 

Transition Widths and Strengths. The widths and strengths of spectroscopic transitions determine the information that can be extracted from a spectmm, and are functions of the molecular parameters summarized in Table 2. Detectivity is deterrnined by spectral resolution and transition strength. Resolution, the abiUty to distinguish transitions of nearly equal wavelength, depends on both the widths of the spectral features and characteristics of the instmmentation. Unperturbed transitions have natural, Av widths owing to the intrinsic lifetimes of the states involved. The full width at... 

Disease States. Rickets is the most common disease associated with vitamin D deficiency. Many other disease states have been shown to be related to vitamin D. These can iavolve a lack of the vitamin, deficient synthesis of the metaboUtes from the vitamin, deficient control mechanisms, or defective organ receptors. The control of calcium and phosphoms is essential ia the maintenance of normal cellular biochemistry, eg, muscle contraction, nerve conduction, and enzyme function. The vitamin D metaboUtes also have a function ia cell proliferation. They iateract with other factors and receptors to regulate gene transcription. 

The terms AG, AH, and AS are state functions and depend only on the identity of the materials and the initial and final state of the reaction. Tables of thermodynamic quantities are available for most known materials (see also Thermodynamic properties) (11,12). 

Dried blends of whole egg and yolk with carbohydrates have sucrose or com symp added to the Hquids before spray-drying. Such carbohydrates (qv) preserve the whipping properties of whole egg and yolk by keeping the fat in an emulsified state. Com symp also gives anticaking characteristics, better flowabiHty, and improved dispersibiHty in water. Dried blends of egg and carbohydrate function weU in emulsified, as weU as unemulsified, sponge cakes. 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

State Functions State functions depend only on the state of the system, not on past history or how one got there. If r is a function of two variables, x and y, then z x,y) is a state function, since z is known once X and y are specified. The differential of z is... 

Themodynamic State Functions In thermodynamics, the state functions include the internal energy, U enthalpy, H and Helmholtz and Gibbs free energies, A and G, respectively, defined as follows ... 

S is the entropy, T the absolute temperature, p the pressure, and V the volume. These are also state functions, in that the entropy is specified once two variables (like T andp) are specified, for example. Likewise,... 

V is specified once T and p are specified it is therefore a state function. 

Approximate calculations of this activation energy have been made in a number of examples using the quanmm theory of molecular binding, by making assumptions concerning the stmcture and paitition functions of the Uansition state molecule. 

Note that this is also a functional of liaAr), Cas(r), and 4 ). Imposing constraints concerning the orthonormality of the configuration state function (C) and one-particle orbitals (pi) on the equation, one can derive the Eock operator from. A based on the variational principle ... 

The thermodynamic stability of a protein in its native state is small and depends on the differences in entropy and enthalpy between the native state and the unfolded state. From the biological point of view it is important that this free energy difference is small because cells must be able to degrade proteins as well as synthesize them, and the functions of many proteins require structural flexibility. 

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